The present embodiments relate to characterizing a point response function (PRF) in single photon emission computed tomography (SPECT). A PRF is the image formed on a detector by a point source in the absence of appreciable attenuation and scatter between the source and the detector. The PRF is used in reconstruction. For reconstructing emissions from a patient, the PRF as a function of location is used. When imaging a finite source (e.g., a patient), the image of function of the patient is generated as a convolution of the PRF with the emissivity (e.g., detected emissions) of the finite source as a function of position.
A three-dimensional (3D) PRF is used to characterize the SPECT imaging systems since the source is close to the detector. The 3D PRF is typically modeled. One simple example is a Gaussian function. The model may be based on emission measurements from a point source, but is an approximation limited in transverse extension and may not properly account for a tail of the PRF. For example, the PRF of the LEHR collimator with Tc-99m used by the Flash3D reconstruction misses ˜20% of the total PRF. Even an effective-aperture model may still miss ˜10% of the PRF in the tail.
The desired accuracy of a 3D PRF depends on the application. For quantitative imaging, which aims to measure an amount of uptake or other characteristic in a volume of interest, the accuracy is desired to be better than 10%, such as aiming for a goal ˜1%. Since the 3D PRF used in reconstruction contributes to the accuracy, the 3D PRF should have the same or similar accuracy demanded of the image. However, the models for PRF, even when based on measurements, do not achieve such accuracy. The 3D PRF may be measured instead such that the response at each location in 3D is provided in tabular form. However, extensive effort is needed to measure a 3D tabular PRF, and the resulting large number of samples (one for each location in 3D) may be difficult to handle in practical image reconstruction.